Macroscopic Approximations to Networks with Applications to Performance Analysis

网络的宏观近似及其性能分析的应用

• 批准号: 9211343
• 负责人: Takis Konstantopoulos
• 金额: $ 9.98万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-15 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9211343&HistoricalAwards=false
• 关键词: Macroscopic; Approximations; Networks; Applications; Performance

The investigation and application of techniques for obtaining macroscopic approximations for communication networks is studied. These approximations are deterministic, described by ordinary differential equations, and stochastic (diffusion), described by stochastic differential equations. The former yield approximations for the time dependent behavior, while the latter quantify the statistical deviations. The techniques consist of a combination of weak convergence and martingale methods. The proposed methods allow for the investigation of networks with service times having not only exponential but also general service time distributions. The transmission rates can be taken to depend on the buffer occupancies, which is important in congestion control applications. The importance of those approximations becomes clear given the non-existence of flexible analytical tools that can give estimates of queue lengths and other performance measures for such (non-product-form) networks. The approximate models, arising via certain limiting procedures, will be used to further study stability issues, settling times and rates of convergence to the steady state. The methods and estimates will be established mathematically and also validated numerically and by simulations.

技术的研究与应用 获得通信网络的宏观近似 研究了这些近似值是确定性的，描述为： 常微分方程和随机（扩散）， 用随机微分方程描述。 前 产生时间依赖行为的近似值，而 后者量化了统计偏差。的技术 由弱收敛和鞅的组合组成 方法.所提出的方法允许调查 网络的服务时间不仅具有指数， 一般服务时间分配。传输速率可以 取决于缓冲区占用率，这一点很重要 在拥塞控制应用中。这些的重要性 由于不存在柔性，近似变得清晰 分析工具，可以提供估计的队列长度， 这种（非产品形式）网络的其他性能测量。 近似模型，通过某些限制程序产生， 将用于进一步研究稳定性问题， 和收敛到稳定状态的速率。的方法和 将以数学方式建立估计值，并进行验证 数字和模拟。